摘要Both diffusion and epidemic are well studied in the stochastic systems and complex networks, respectively. Here we combine these two fields and study epidemic diffusion in complex networks. Instead of studying the threshold of infection, which was focused on in previous works, we focus on the diffusion behaviour. We find that the epidemic diffusion in a complex network is an anomalous superdiffusion with varying diffusion exponent γ and that γ is influenced seriously by the network structure, such as the clustering coefficient and the degree distribution. Numerical simulations have confirmed the theoretical predictions.
Abstract：Both diffusion and epidemic are well studied in the stochastic systems and complex networks, respectively. Here we combine these two fields and study epidemic diffusion in complex networks. Instead of studying the threshold of infection, which was focused on in previous works, we focus on the diffusion behaviour. We find that the epidemic diffusion in a complex network is an anomalous superdiffusion with varying diffusion exponent γ and that γ is influenced seriously by the network structure, such as the clustering coefficient and the degree distribution. Numerical simulations have confirmed the theoretical predictions.
[1] Albert R and Barabasi A L 2002 Rev. Mod. Phys. 74 47 [2] Boccaletti S et al %, Latora V, Moreno Y, Chavez M and Hwang D U2006 Phys. Rep. 424 175 [3] Pastor-Satorras R and Vespignani A 2001 Phys. Rev. Lett. 86 3200 [4] Joo J and Lebowitz J L 2004 Phys. Rev. E 69 066105 [5] Barthelemy M and Barrat A 2005 J. Theor. Biol. 235 275 [6] Zheng D F et al %, Hui P M, Trimper S and Zheng B2005 Physica A 352 659 [7] Liu Z, Lai Y C and Ye N 2003 Phys. Rev E 67 031911 [8] Naim E B 2004 Phys. Rev. E 69 050901 [9] Newman M E J 2002 Phys. Rev. E 66 016128 [10] Yan G et al %, Zhou T, Wang J, Fu Z Q and Wang B H2005 Chin. Phys. Lett. 22 510 [11] Zhang H, Liu Z and Ma W 2006 Chin. Phys. Lett. 23 1050 [12] Eguiluz V M and Klemm K 2002 Phys. Rev. Lett. 89 108701 [13] Liu Z and Hu B 2005 Europhys. Lett. 72 315 [14] Crank J 1970 The Mathematics of Diffusion (Oxford: Clarendon) [15] Metzler R et al %, Barkai E and Klafter J1999 Phys. Rev. Lett. 82 3563 [16] Rangarajan G and Ding M 2000 Phys. Rev. E 62 120 [17] Holme P and Kim B J 2002 Phys. Rev. E 65 026107
2007, Vol. 24 
